{
  "id": "2204.07658",
  "version": "v1",
  "published": "2022-04-15T21:59:42.000Z",
  "updated": "2022-04-15T21:59:42.000Z",
  "title": "An anticyclotomic Euler system for adjoint modular Galois representations",
  "authors": [
    "Raúl Alonso",
    "Francesc Castella",
    "Óscar Rivero"
  ],
  "comment": "24 pages, comments welcome",
  "categories": [
    "math.NT"
  ],
  "abstract": "Let $K$ be an imaginary quadratic field and $p$ a prime split in $K$. In this paper we construct an anticyclotomic Euler system for the adjoint representation attached to elliptic modular forms base changed to $K$. We also relate our Euler system to a $p$-adic $L$-function deduced from the construction by Eischen-Wan and Eischen-Harris-Li-Skinner of $p$-adic $L$-functions for unitary groups. This allows us to derive new cases of the Bloch-Kato conjecture in rank zero, and a divisibility towards an Iwasawa main conjecture.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-04-15T21:59:42.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11R23",
      "11F85",
      "14G35"
    ],
    "keywords": [
      "adjoint modular galois representations",
      "anticyclotomic euler system",
      "elliptic modular forms base",
      "imaginary quadratic field",
      "iwasawa main conjecture"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 24,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}